Characterizing population dynamics

Slides:



Advertisements
Similar presentations
Population Ecology & Demography; Leslie Matrices and Population Projection Methods Introduction to linking demography, population growth and extinction.
Advertisements

9 Population Growth and Regulation. 9 Population Growth and Regulation Case Study: Human Population Growth Life Tables Age Structure Exponential Growth.
Population Ecology: Growth & Regulation Photo of introduced (exotic) rabbits at “plague proportions” in Australia from Wikimedia Commons.
Population ecology Chapter 53- AP Biology.
The Tools of Demography and Population Dynamics
Chapter 10 Population Dynamics
DEMOGRAPHY The study of birth and death processes
Population Ecology Population - group of individuals of the same species living in the same general area. – They must rely on the same resources, have.
Population Ecology Ch 52.
Are we over carrying capacity?
Population Biology: PVA & Assessment Mon. Mar. 14
POPULATION ECOLOGY.
Population Ecology u Study of the factors that affect population size and composition.
STRUCTURED POPULATION MODELS
Chapter 52 Population Ecology. Population ecology - The study of population’s and their environment. Population – a group of individuals of a single species.
Organisms at different life stages can have vastly different reproduction and mortality rates: Juveniles: often high mortality risk and no reproduction.
What is a population? Within a given area where the scale of the area is study-dependent Localised group of individuals of the same species e.g. population.
Demography Factors that affect growth & decline of populations
The Leslie Matrix How do we take the differences in survivorship and fecundity into account to ‘project’ the future of the population? The mechanism is.
55.2 How Do Ecologists Study Population Dynamics? To understand population growth, ecologists must measure population processes as well as population traits.
Measuring and Modeling Population Change SBI4U. Demography The statistical study of the processes that change the size and density of a population through.
Dynamic biological processes influence population density, dispersion, and demographics Chapter 53, Section 1.
Chapter 52: Population Ecology. Population Ecology  Study of the factors that affect population size and composition.  Population Individuals of a single.
1 Population Ecology. 2 Environmental Variation Key elements of an organism’s environment include: – temperature – water – sunlight – Soil – Classical.
Ecology 8310 Population (and Community) Ecology
What is Ecology? Scientific study of the interactions of organisms with their abiotic and biotic environments in order to understand the distribution.
Chapter 40 Population Ecology and Distribution of Organisms – Part 2.
 What is the density of a population?  The number of individuals per unit area  Dispersion is how they spread out in that area  What are the three.
Matrix modeling of age- and stage- structured populations in R
1 Population Ecology. 2 Environmental Variation Key elements of an organism’s environment include: Key elements of an organism’s environment include:
Section 1: Population Dynamics
POPULATION ECOLOGY All of the data that can be collected about a population of species in one area.
Dynamics of Ecosystems: Population Ecology
Population Ecology.
FW364 Ecological Problem Solving Class 15: Stage Structure
Ch. 54 Warm-Up (Review) Sketch an exponential population growth curve and a logistic population growth curve. What is an ecological footprint? What.
Chapter 4 Population Ecology
Presentation topics Agent/individual based models
Population Ecology.
Ch. 40b Warm-Up (Review) Sketch an exponential population growth curve and a logistic population growth curve. What is an ecological footprint? What.
POPULATION ECOLOGY.
Chapter 4 Population Ecology
Chapter 53 Population Ecology.
Lecture #23 Date _______ Chapter 52 ~ Population Ecology.
Chapter 53 ~ Population Ecology
Population A group of individuals of the same species that interact with each other in the same place at the same time Metapopulation A population of populations,
FW364 Ecological Problem Solving Class 16: Stage Structure
Population Dynamics Chapter 52.
Lecture #23 Date _______ Chapter 52 ~ Population Ecology.
Matrix Population Models
Wildlife Population Analysis
Chapter 52 ~ Population Ecology
Ecology! Sections
Population Dynamics Chapter 6.
Ch. 53 Warm-Up (Review) Sketch an exponential population growth curve and a logistic population growth curve. What is an ecological footprint? What.
 Population  group of individuals of same species in same general area
Population Ecology.
The number of organisms per unit area
Ch. 40b Warm-Up (Review) Sketch an exponential population growth curve and a logistic population growth curve. What is an ecological footprint? What.
Ch. 53 Warm-Up (Review) Sketch an exponential population growth curve and a logistic population growth curve. What is an ecological footprint? What.
Ch. 52 Warm-Up (Review) Sketch an exponential population growth curve and a logistic population growth curve. What is an ecological footprint? What.
Biology, 9th ed, Sylvia Mader
Ch. 40b Warm-Up (Review) Sketch an exponential population growth curve and a logistic population growth curve. What is an ecological footprint? What.
Lecture #23 Date _______ Chapter 52 ~ Population Ecology.
Introduction to Populations
Population Ecology.
Chapter 40b Population Ecology.
Chapter 4 Population Ecology
Warm-Up (Review) Sketch an exponential population growth curve and a logistic population growth curve. What is an ecological footprint? What are ways.
Chapter 6 Population Biology
Presentation transcript:

Characterizing population dynamics How fast does a population increase/decrease? (rate of change) What will the population size be next year? (management) Need to summarize Births & Deaths (age structure) of a population Cohort Life Tables follow one group from birth until the last one dies Static Life Table census population for abundance in each age/stage combined with estimates of survival and reproductive output by age/stage Limitations? Must be able to age/stage each organism (challenging, uncertainty)

Survivorship curves

Structured demographic models Translate variation in individuals (measureable) to population dynamics (less measurable) Structured around life-history schedules of different species or populations Demography (vital rates by age, sex, stage, size, etc.) captures both the dynamics & structure of populations Widely adopted to evaluate species vulnerability (Population Viability Analysis, late 1990’s )

Life history components Maturity- age at 1st reproduction Mosquito (14 days), Desert tortoise (25-30 years) Parity- # of episodes for reproduction Sockeye salmon (1), White footed mouse (4-12) Semelparity vs. Iteroparity (annual, perennial) Fecundity- # offspring/episode Elephant (1), Western Toad (8,000-15,000) Aging/Senescence- survival/life span - Fruit fly (35 d), Blue Whale (80-90 y)

Not all combinations are possible... Log 2 eggs x 2 / yr 20d parental care Lifespan 2-3yr Log 1 egg/ ~2yr 9 mo. parental care Lifespan >60yr

Life history of Cascades frogs 4 life stages: Embryonic: lasts 1-3 weeks, 0-80 (~60)% survival Larval (tadpole): lasts 8-12 weeks ~50% survival Juvenile (metamorph): lasts 2-3 years (10-40??)% annual survival Adult: lasts 8-20+ years, 300-700 offspring/yr 70-80% annual survival Rana cascade

Life history diagram for Cascades frogs Vital rates, also called transition probabilities 300-700/yr Embryos Larvae Juveniles Adults x 1 - x 0.6 0.5 0.7-0.8 0.1-0.4 2-3 yr 4-7 yr 1 yr

Life history of elephants 5 life stages: Yearling: 80% survival, lasts 1 year Pre-reproductive: 98% survival, lasts 15 year Early reproductive: 98% survival, lasts 5 years, 0.08 offspring/yr Middle reproductive: 95% survival, lasts 25 years, 0.3 offspring/yr Post-reproductive: 80% survival, 5-25 years

Life history diagram for elephants 0.1/yr 0.08/yr 0.8 0.98 0.95 Post-reproductive Pre-reproductive Middle age Early Repro Yearling x x x 1- x 1- x 1- x 1 yr 15 yr 5 yr 25 yr 5-25 yr

Other ways to depict life cycle Age-based Stage-based Size-based

Life histories Bubble diagrams summarize average life history events with fixed time steps (survival per week, year, decade) Result of natural selection Organisms exist to maximize lifetime reproductive success Represent successful ways of allocating limited resources to carry out various functions of living organisms Survival, growth, reproduction

Questions we can answer with age/stage structured population models: How much harvest of a population can occur while still have less than an X% chance of extinction? What life history stages should conservation (or eradication) efforts be focused on to achieve the biggest change in population size/growth rate? How many populations of a species need be preserved to ensure reasonable protection from periodic local extinctions and infrequent catastrophic events? Which life-history strategies are more or less vulnerable to exploitation and extinction? Is it worth the effort to try and recover a particular population, or is it so likely to go extinct that limited resources should be invested elsewhere? and hundreds more!

Single species population growth models

Matrix population models

Basic matrix construction 1 2 3 a21 a32 a33 a13 aij transition prob. to row i from column j (per timestep) Columns = j (from) Rows = i (to)

Basic matrix construction 1 2 3 a21 a32 a33 a13 If there were only one class, what would this look like? x Matrix (A) x population vector (nt) = population vector (nt+1) Underlying this model is an assumption of EXPONENTIAL growth

3 x 3 age-structured matrix (also called Leslie matrix) P=probability of surviving from one age to the next F=fecundity of individuals at each age In this case, there are two pre-reproductive years (maturity at age three) *only need one subscript here because indivds must move ages each time step See any inconsistency here?

4 x 4 size-structured matrix (also called Lefkovitch matrix) Pij=probability of growing from one size to the next or remaining the same size (need subscripts to denote new possibilities) F=fecundity of individuals at each size In this case, there are three pre-reproductive sizes (maturity at age four). **additional complexities like shrinking or moving more than one class back or forward is easy to incorporate

Matrix multiplication 1 2 3 Semipalmated sandpiper data from Hitchcock & Gatto-Trevor (1997) Three stages (1,2,3+ yrs), with reproduction at each stage. a21 a32 a33 1 2 3 x nt per ha Average matrix 1 2 3

Matrix multiplication 1 2 3 x nt How do we calculate the number present in each class next year (nt+1)? =

Matrix multiplication nt n(1) n(2) n(3) n(4) n(5) n(6) n(7) n(8)

Matrix multiplication nt n(1) n(2) n(3) n(4) n(5) n(6) n(7) n(8) Is this population declining/increasing/stable?

Matrix multiplication nt n(1) n(2) n(3) n(4) n(5) n(6) n(7) n(8) = sum (n2) / sum(n1) What’s the proportional change in the population from one time to the next? = lambda (λ) (0.639)

Matrix multiplication Semipalmated sandpiper data from Hitchcock & Gatto-Trevor (1997) nt Average matrix Is this population declining/increasing/stable? Dominant eigenvalue (1) *stable environment or average matrix* Asymptototic measure of geometric, density-independent population growth rate Is the population at a stable distribution of stages/ages? Dominant eigenvector (w)

What to do with a deterministic matrix? Fixed environment assumption is unrealistic. BUT… can evaluate the relative performance of different management/conservation options can use the framework to conduct ‘thought experiments’ not possible in natural contexts can ask whether the results of a short-term experiment/study affecting survival/reproduction could influence population dynamics

A short detour for an example

low UV-B moderate UV-B high UV-B % survival -UV +UV -UV +UV % survival +UV % survival -UV How does egg mortality change across a natural gradient of UV-B exposure? 28

29

?? UV 10,000 eggs 3,000 larvae 6,000 larvae 100 juveniles dispersal UV ?? 10,000 eggs 6,000 larvae 3,000 larvae adults (4-10 years) eggs (1-3 weeks) Talk about variability in recruitment to adult population “Population” in most cases includes many breeding sites across the landscape larvae (8 weeks-3+ years) 100 juveniles 30

What to do with a deterministic matrix? Fixed environment assumption is unrealistic. BUT… can evaluate the relative performance of different management/conservation options can use the framework to conduct ‘thought experiments’ not possible in natural contexts can ask whether the results of a short-term experiment/study affecting survival/reproduction could influence population dynamics *can evaluate the relative sensitivity of  to different vital rates

Matrix element sensitivities Semipalmated sandpiper data from Hitchcock & Gatto-Trevor (1997) nt Average matrix Reproductive value Sensitivity of 1 to element aij is Sij Prop in j @ stable age constant

Matrix element sensitivities Semipalmated sandpiper data from Hitchcock & Gatto-Trevor (1997) nt Average matrix Sensitivity analysis of a deterministic matrix (by brute force): Vary vital rates individually (small change vs. biologically realistic range?) Re-calculate deterministic 1 Plot change in each rate versus change in 1

Matrix element sensitivities Semipalmated sandpiper data from Hitchcock & Gatto-Trevor (1997) nt Average matrix Sensitivity analysis of a deterministic matrix: X

Matrix element sensitivities Semipalmated sandpiper data from Hitchcock & Gatto-Trevor (1997) nt Average matrix Relative sensitivities (comparable across vital rates) called Elasticities proportional change of vital rates compared to proportional change in lambda Why does might this matter?